Subharmonic and Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Rotor

Abstract

Subharmonic and summed-and-differential harmonic oscillations of a nonlinear rotating shaft system where an unsymmetrical rotor is mounted on a shaft with circular cross section are treated. It becomes clear theoretically that the resonance curves of subharmonic oscillations of order 1/2 and summed-and-differential harmonic oscillations are classified in to four types. Therefore, similarly to those of an unsymmetrical shaft system reported previously, stable oscillation, unstable oscillation, or no oscillation appears. In an experimental apparatus in which single-row deep groove ball bearings were used, we observed the same types of the resonance curves as the theoretical results by changing the assembly of the apparatus and the size and location of the existing unbalance.